ELECTRICITY.pdf

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ELECTRICITY.pdf

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ELECTRICITY




Electricity and its Effect (notations)


Physical Quantity

Symbols

SI unit


Voltage (potential difference)

V

Volt (V)


Power

P

Watt (W)


Charge

Q

Coulomb (C)


Work or Energy

W

Joule (J)


Resistance

R

Ohm (

)


Current

I

Ampe
re (A)


Resistivity



Ohm metre (


m)



Laws of electric forces:


(i)

Like charges repel and unlike charges attract each other.


(ii)

Charges of a conductor reside on its outer surface.


Current:


The rate of flow of charges (Q) through a conductor is cal
led current (I) and is given
by.


Current =
Time
charge

or
t
Q
I
=
. The SI unit of current is ampere (A).

1 Ampere
second
1
coulomb
1
=


The current flowing through a circuit is measured by a device called ammeter.
Ammeter is

connected in series with the conductor. The direction of the current is taken as the
direction of the flow of positive charge and opposite to the flow of electrons through the
conductor.


Electric cell:

It is the simplest form of arrangement to maintain a

constant potential
difference between two points.


Electromotive force:

The potential difference at the terminals of cells in an open
circuit is called electromotive force (emf) and is denoted by letter E.


Potential difference is the work done in bringin
g a unit charge from one place to
another.

charge
work
Difference

Potential
=
,
(C)

Coulomb
1
)
(J
Joule
1
(V)
Volt
1
=



Ohms law:

At any constant temperature the current (I) flowing through a conductor is
directly proportional to the potential difference (V) across it. Mathematical
ly,



I


V

vice
-
versa

V


I


or

V = RI




R
V
I
I
V
R
=
=
,


where

R


Resistance,

V


Voltage (P.D.),

I


Current



Symbols of a few commonly used components in Circuit Diagrams


Component

Symbol

Component

Symbol

An electric cell



Electric bulb



Battery of cells



A resistance



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Plug key or switch
(open)



or


Variable resistance

(R
heostat)


or


A closed plug or
switch



or


Ammeter


A

+




A wire joint



Voltmeter


V

+




Wires crossing



Galvanometer


G

+






Resistance:

Resistance is a property of a conductor by virtue of which it opposes the
flow of electricity through it. Resistance is measured in Ohms

(

)
. Resistance is a scalar
quantity.


Conductor:

Low
-
resistance material which allows the flow of electric current through
it is called a conductor. All metals are conductors except Hg and Pb etc.


Resistor:
High
-
resistance materials are called resistors. Resistors become hot when
current fl
ows through them (nichrome wire is a typical resistor).


Insulator:

A material which does not allow heat and electricity to pass through it is
called an insulator. Rubber, dry wood etc., are insulators.


Equivalent Resistance:

A single resistance which can

replace a combination of
resistance
s

such that current through the circuit remains the same is called equivalent
resistance.


Law of Combination of Resistances in Series:

When number of resistances are
connected in series, the equivalent resistance is equ
al to the sum of the individual resistances.

3
2
1
V
V
V
V
+
+
=


3
3
2
2
1
1
,
,
,
IR
V
IR
V
IR
V
IR
V
=
=
=
=


3
2
1
IR
IR
IR
IR
+
+
=


n
R
R
R
R
R
+
+
+
=
.....
3
2
1





Things to remember in series connection


(a)

When a number of resistances are connect
ed in series, the equivalent or resultant
resistance is equal to the sum of individual resistances and resultant resistance is greater than
any individual resistance.

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(b)

If
n

resistances each of value
R

are connected in series, the equivalent resistance
R
e

is given by:





R
e

=
R

+
R

+
R

..........
n

times





R
e

=
nR






R
e

= Number of resistors × resistance of each resistor


(c)

Equal current flows through each resistance and it is also equal to the total current
in the circuit. This is because there i
s no other path along which the current can flow.


(d)

The potential difference across the ends of the combination is distributed across
the ends of each of the resistances. The potential difference across any one of the resistances
is directly proportiona
l to its resistance.


(e)

The equivalent resistance when used in place of the combination of resistances
produces the same current with the same potential difference applied across its ends.


(f)

When two or more resistances are joined in series, the resul
t is the same as
increasing the length of the conductor. In both cases the resultant resistance is higher.


(g)

In a series combination, the equivalent resistance is greater than the greatest
resistance in the combination.


Law of Combination of Resistance
s in Parallel:
If resistance
.....
,
,
,
3
2
1
R
R
R

etc are
connected
in parallel

then the equivalent resistance (
R
) is given by

3
2
1
I
I
I
I
+
+
=


3
3
2
2
1
1
,
,
,
R
V
I
R
V
I
R
V
I
R
V
I
=
=
=
=


3
2
1
R
V
R
V
R
V
R
V
+
+
=


n
R
R
R
R
R
1
.....
1
1
1
1
3
2
1
+
+
+
=





Things to remember in parallel connection


(a)

When a number of resistances are connected in parallel, the reciprocal of the
equivalent or resultant resistance is equal to the sum of reciprocals of the individual
resistances and is always smaller than th
e individual resistances. This is because there are a
number of paths for the flow of electrons.

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(b)

If there are n resistances connected in parallel and each resistance has a value
of

R





n
R
R
R
R
e
..........
1
1
1
1
+
+
=

times





R
n
R
e
=
1






n
R
R
e
=





resistors

of

number
resistor

each

of

Resistance
=
e
R


(c)

The potential difference across each resistance is the same and is equal to the
total potential difference across the combination.


(d)

The main current divides itself and a different current flows th
rough each resistor.
The maximum current flows through the resistor having minimum resistance and vice versa.


(e)

If an equivalent resistance
R
e

is connected in place of combination, it produces
the same current for the same potential difference applied a
cross its ends.


(f)

In a parallel combination, the equivalent resistance is lesser than the least of all
the resistances.


(g)

If two resistances
R
1

and
R
2

are connected in parallel then





2
1
2
1
2
1
1
1
1
R
R
R
R
R
R
R
e
+
=
+
=





s
resistance

two

of

Sum
s
resistance

two

of

Product
2
1
2
1
=
+
=
R
R
R
R
R
e


(h)

If ther
e are
n

resistors each of resistance
R
.

Let
R
S

be the resultant resistance of
series combination and
R
p

be the resultant resistance of parallel combination.




Then,


R
S

= nR







R
p

=
n
R






2
/
n
n
R
nR
R
R
p
S
=
=
.



Electrical
energy:

Capacity of the flowing electricity to do work is called its electrical
energy.


Electrical energy (work) =
R
t
V
Pt
Rt
I
t
I
V
2
2
=
=
=


The SI unit of electrical energy is Joule.

One Joule is the amount of energy
consumed when an electrical appliance
of one watt rating is used for one second. The
commercial (practical) unit of electrical energy is kilowatt
-
hour (kWh).




Power,
R
V
R
I
VI
t
W
P
2
2
=
=
=
=

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The SI unit of electric power is watt (W).

The power of a machine doing work at the
rate of 1 Joule p
er second is equal to one watt.


Electrical energy = Electrical power × Time.


Important Formulae:


1.

Coulomb’s law




2
2
1
r
q
q
K
F


=

(
k

is constant of
proportionality
)


1
q

and
2
q

= two electric charges




r

= distance between two electric charges




F

= Force

2.

V
W
Q
Q
V
W
Q
W
V
=

=
=
;
;


.
.
d
p
V
=

W

= work done,
Q

= Quantity of charge transferred

3.

R
V
I
I
V
R
I
R
V
=
=

=
;
;


V

=
pd

;
R

= Resistance,
I

= current.

4.

l
A
R
A
I
R

=



=
;

R

= Resistance;
l

= length;
A

= Area of cross section;


= rho, a constant known as
resistivity

5.

Series combination
n
R
R
R
R
R
+
+
+
=
.....
3
2
1

6.

Parallel combination
n
R
R
R
R
R
1
.....
1
1
1
1
3
2
1
+
+
+
=



For equal resistances


nR
Rs
=

(For series co
nnection)


n
R
Rp
=

(For parallel connection)


2
n
Rp
Rs
=


Rs
= Effective resistance i
n

series


Rp

= Effective resistance i
n

parallel



n

= number of resistors



R

= Resistance of each resistor

7.


Time
consumed
Energy
time
work
Power
;
=
=
=
t
W
P

8
.


W

=
V

×
I

×
t

; Power =
potential difference

× current × time





)
(
2
Rt
I
W
=











=
R
t
V
W
2

9.

P

=
V

×
I

; Power =
potential difference

× current

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10.

R
I
P

=
2

; Power =
resistance
(current)
2


11.

R
V
P
2
=

;
resistance
)

difference

(potential
Power
2
=

12.

Electric energy =
P

×
t

; electric energy = power × time



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